Semiconductor Plasma Research Articles

Effect of spin quantum force on lower and upper hybrid waves’ instability under the influence of an electron beam in a magnetized semiconductor plasma

Effect of spin quantum force on lower and upper hybrid waves’ instability under the influence of an electron beam in a magnetized semiconductor plasma

Modulation instability of magnetosonic waves in semiconducting quantum plasma considering Fermi degenerate pressure, exchange correlation potential, and Bohm potential

This study investigates the modulation instability of magnetosonic waves in a semiconducting quantum plasma system. Utilizing the quantum hydrodynamic model, we derive the nonlinear Schrödinger equation and its solution through the reductive perturbation technique. The growth rate of modulation instability for magnetosonic waves has been derived. This study incorporates various quantum corrections, including Fermi degenerate pressure, exchange-correlation potential, and Bohm potential. We study the bright soliton profiles of magnetosonic waves, and additionally, we conduct graphical analyses of the linear dispersion relation and the product of the dispersive coefficient (P) and nonlinear coefficient (Q) of the nonlinear Schrödinger equation. It has been found that magnetosonic waves exhibit modulation instability within specific parameter ranges of the semiconductor plasma and at certain wavelength regimes. Further, we present a comparative study between GaSb and InSb semiconducting plasma systems. The exchange-correlation potential and Fermi degenerate pressure have significantly impacted the modulation instability growth rate, whereas the effect of the Bohm potential is much lower.

Modeling and control of L-type network impedance matching for semiconductor plasma etch

The plasma process plays a pivotal role in the semiconductor industry, facilitating the creation of transistors and memory storage cells. This fourth state of matter is achieved by energizing a gas with radio-frequency electrical power, initiating and maintaining a stable plasma during the process cycles. Given that plasma behaves as an impedance component, an impedance-matching network becomes essential for optimizing power transfer from the source to the load (plasma). While various control strategies have been proposed for different network configurations, such as L, T, and Π networks, our work focuses on the L-type network due to its simplicity and extensive application in this domain. Several significant challenges have been identified in the existing literature, including slow dynamics, a non-monotonic decline in the reflected power, and substantial deviation in the capacitors’ path. These issues collectively impact the overall performance of the matching control system. In this article, we present a new methodology to obtain a nonlinear state-space model of the matching network for its analysis and design a proportional-integral combined with feedforward control and a control Lyapunov-barrier function to assess their effectiveness in achieving convergence to the desired matching value and guiding the path of the capacitors. These approaches aim to mitigate the recurring issues caused by capacitors moving in the wrong direction, thus improving the stability and efficiency of the impedance-matching process over time.

Explainable artificial intelligence-based evidential inferencing on process faults in plasma etching

The fault detection and classification (FDC) modeling proposed in this study is a research approach that is intended to improve the performance of plasma process models by leveraging optical emission spectroscopy (OES) data containing plasma information (PI) and enhancing model interpretability using explainable artificial intelligence (XAI) algorithms. Status variable identification data that included normal and abnormal states of bias power, pressure, SF6 gas flow, and O2 gas flow were collected during a silicon etching process with SF6, O2 gas plasma. Additional variables were derived from the OES data and included additional PI, such as O and F radicals, which were computed using actinometry, and electron temperature and electron density computed using the line ratio method. By building a high-performance FDC model and interpreting its results using XAI algorithms, we propose solutions to the limitations of the FDC model in semiconductor plasma processes.

Numerical impedance matching via extremum seeking control of single-frequency capacitively coupled plasmas

Abstract Impedance matching is a critical component of semiconductor plasma processing for minimizing the reflected power and maximizing the plasma absorption power. In this work, a more realistic plasma model is proposed that couples lumped element circuit, transmission line, and particle-in-cell (PIC) models, along with a modified gradient descent algorithm (GD), to study the impact of presets on the automatic matching process. The effectiveness of the proposed conceptual method is validated by using a single-frequency capacitively coupled plasma as an example. The optimization process with the electrode voltage and the reflection coefficient as the objective function and the optimized state, including plasma parameters, circuit waveforms, and voltage and current on transmission lines, is provided. These results show that the presets, such as initial conditions and objective functions, are closely related to the automatic matching process, resulting in different convergence speeds and optimization results, proving the existence of saddle points in the matching network parameter space. These findings provide valuable information for future experimental and numerical studies in this field.

O razrushenii resheniya odnoy zadachi dlya sobolevskogo uravneniya s nekoertsitivnym istochnikom

We consider an initial–boundary value problem for a nonlinear Sobolev-type second-order differential equation with a noncoercive source describing the behavior of charges in a semiconductor plasma in an external field. The local solvability of this problem is proved, and upper bounds are obtained for the solution blow-up time.

Consequence of head-on collision of ion acoustic waves in unmagnetized plasmas having generalized (r, q) distributed electrons and positrons

To explore the effect of the head-on collision (such as phase shifts, collisional processes, and production of solitons) of ion-acoustic waves (IAWs), a collisionless unmagnetized electron-positron-ion (e-p-i) plasma is considered. The electrons and positrons follow the generalized () distribution. To do this, using the extended Poincaré-Lighthill-Kuo (ePLK) approach, the two-sided Korteweg-de Vries (KdV) equations and phase shifts are derived. The main aim of this study is to investigate the consequence of spectral indices and on both the negative and positive phase changes following an IAW-to-IAW collision. It is found that for the effects of the spectral indices of electrons and positrons both positive and negative phase shifts after head-on collisions are modified. The compressive (only hump-shaped) as well as rarefactive (both hump and dip-shaped) solitons become produced for the effect of spectral indices. The results obtained in the study may be helpful to understand the collision processes as well as the consequence of the head-on collision of IAWs in electron-positron-ion plasmas in the ionosphere, auroral acceleration regions, solar wind, Saturn rings, active galactic nuclei, polar cup of fast rotating neutron stars, semiconductor plasmas, and intense laser fields as well as in laboratory experiment.

Quantum effects on dispersion, threshold and gain characteristics of Brillouin scattered Stokes mode in ion-implanted semiconductor plasmas

Quantum effects (QEs) on the dispersion, threshold, and gain characteristics of the Brillouin scattered Stokes mode (BSSM) in ion-implanted semiconductor plasmas are analytically investigated using coupled mode theory. Taking into account that the origin of stimulated Brillouin scattering lies in nonlinear induced polarisation of the medium, expressions are derived for complex effective Brillouin susceptibility (due to electrons and implanted colloids) and consequently the threshold pump amplitude and the gain constant of BSSM. Inclusion of QEs is done via quantum correction term in the hydrodynamic model of semiconductor plasmas. QEs modify the dispersion, threshold and gain characteristics of BSSM in ion implanted semiconductor plasmas. In contrast to the threshold and gain characteristics of BSSM, which are impacted only by electrons and are unaffected by implanted charged colloids, the Brillouin susceptibility caused by implanted colloids has a significant impact on the dispersion characteristics of BSSM. Finally, an extensive numerical study of the n- InSb/CO2 laser system is performed for two different cases: (i) without QEs and (ii) with QEs. In both cases, the analysis offers two achievable resonances, at which the changes of sign as well as an enhancement of real part of effective Brillouin susceptibility and an enhancement of effective Brillouin gain constant are obtained. When QEs are included in the analysis, the entire spectrum shifts towards decreased levels of electron and colloidal carrier concentration.

Method for improving dry etching end point detection based on change in time accumulation correlation of plasma emitting wavelengths

This study proposes an optical emission spectroscopy (OES) analysis methodology to improve the ability to detect etching endpoints during high-level semiconductor plasma etching processes. Representative etching endpoint detection methods using single wavelength intensity or multiple wavelength intensity ratio changes include a low signal-to-noise ratio, high plasma instability, a small etching open area, and weak by-product emission signal problems due to deep etching under high-level process conditions such as high aspect ratio contact etching (HARC). As a result, it is difficult to detect the etching endpoint due to the very small or noisy change in the intensity over time due to the process progress of the wavelength selected by OES to detect the etching endpoint. In this study, a method of deriving an accumulative time correlation value according to process progress between selected wavelengths was developed by selecting all wavelengths observed in a specific wavelength region such as ultraviolet region in a spectrum emitted from plasma during a plasma etching process. After classifying the entire correlation signal groups derived as a pair of two intensity peak wavelengths into a dynamic time wrapping algorithm, the intensity change rate of the signal according to the process time was observed by selecting the signal with the most sensitive time change rate during the process. During the vertical nand flash memory manufacturing process, a test wafer for the purpose of detecting the etching endpoint was manufactured and evaluated under the conditions of the cell metal contact etching process, which is a high-level HARC etching process. As a result, it was confirmed that the signal selected by deriving the time accumulative correlation method had a high intensity change rate and a signal-to-noise ratio over time compared to a single wavelength or a plurality of wavelength ratio signals. The method proposed in this study is expected to contribute to process optimization by contributing to improving the ability to detect etching endpoints in high-level plasma etching processes in the future.

Reduced amount of contamination particle generated by CF4/Ar/O2 plasma corrosion of Y2O3 materials: Influence of defluorination process

Y2O3 coatings during atmospheric plasma spray (APS) processes are used to suppress the corrosion of internal process chamber parts for semiconductor plasma etching. Highly corrosive fluorine-based plasma corrodes the surface, causing contamination particle and process drift, which are the main causes of yield reduction. In this paper, defluorination is proposed to reduce the amount of contamination particle generation by removing the YOxFy layer on the surface of APS-Y2O3 material after plasma etching. After exposure to CF4/Ar/O2 plasma, chemical–mechanical polishing occurred using KOH, surfactant, and piranha solutions, respectively. The highest and lowest defluorination efficiencies were obtained with the piranha and surfactant solutions, respectively. The results were validated by field-emission scanning electron microscopy, energy-dispersive X-ray spectroscopy, and X-ray photoelectron spectroscopy. In particular, the piranha solution generated the lowest amount of contamination particles and lowest amount of etching. In contrast, the thickness reduction due to the defluorination process resulted in the highest breakdown voltage among the surfactant solutions, thereby prompting optimization studies. Finally, the mechanisms of the plasma etching and defluorination processes were derived, and a new method for controlling the amount of contamination particle generation was presented.

Mid-Infrared Radiation from Semiconductor Plasmas Using Extraordinary Mode of Lasers

Mid-Infrared Radiation from Semiconductor Plasmas Using Extraordinary Mode of Lasers

Effects of changing thermal conductivity on photothermal excitation in non-local semiconductor material subjected to moisture diffusion and laser pulses

A novel model is presented in this study for the situation of wave interference in a non-local stimulated semiconductor medium, including thermal, plasma, and elastic waves. Moisture diffusion in one dimension (1D) has been included in the governing equations by varying the non-local medium's thermal conductivity under the impact of laser pulse according to the non-Gaussian temporal profile. The dimensionless model was characterized by linear transformations. Analytical solutions were obtained by applying Laplace transforms to a description of the governing equations based on the photo-thermoelasticity theory based on moisture diffusivity and variable thermal conductivity. When applying certain of the circumstances (thermal ramp type and non-Gaussian plasma shock), linear solutions are achieved in the time domain using various numerical techniques based on inverse Laplace transforms. Some of the physical variables being studied are visually shown via numerical simulation. The present investigation has produced numerous important concrete instances. Using graphs and theoretical descriptions, several contrasts are drawn, while certain physical factors, such as relaxation durations, changing thermal conductivity, non-local parameters, and reference moisture values, are in play.

Violation of Neumann Problem’s Solvability Condition for Poisson Equation, Involved in the Non-Linear PDEs, Containing the Reaction-Diffusion-Convection-Type Equation, at Numerical Solution by Direct Method

In this paper, we consider the 3D problem of laser-induced semiconductor plasma generation under the action of the optical pulse, which is governed by the set of coupled time-dependent non-linear PDEs involving the Poisson equation with Neumann boundary conditions. The main feature of this problem is the non-linear feedback between the Poisson equation with respect to induced electric field potential and the reaction-diffusion-convection-type equation with respect to free electron concentration and accounting for electron mobility (convection’s term). Herein, we focus on the choice of the numerical method for the Poisson equation solution with inhomogeneous Neumann boundary conditions. Despite the ubiquitous application of such a direct method as the Fast Fourier Transform for solving an elliptic problem in simple spatial domains, we demonstrate that applying a direct method for solving the problem under consideration results in a solution distortion. The reason for the Neumann problem’s solvability condition violation is the computational error’s accumulation. In contrast, applying an iterative method allows us to provide finite-difference scheme conservativeness, asymptotic stability, and high computation accuracy. For the iteration technique, we apply both an implicit alternating direction method and a new three-stage iteration process. The presented computer simulation results confirm the advantages of using iterative methods.

Stability of the planar rarefaction wave to three-dimensional full compressible Navier–Stokes–Poisson system

A full compressible Navier–Stokes–Poisson system models the motion of viscous ions under the effect of variable temperature and plays important roles in the study of self-gravitational viscous gaseous stars and in simulations of charged particles in semiconductor devices and plasmas physics. We establish the time-asymptotic nonlinear stability of a planar rarefaction wave to the initial value problem of a three-dimensional full compressible Navier–Stokes–Poisson equation when the initial data are a small perturbation of the planar rarefaction wave. The proof is given by a delicate energy method, which involves highly non-trivial a priori bounds due to the effect of the self-consistent electric field. This appears as the first result on the nonlinear stability of wave patterns to the full compressible Navier–Stokes–Poisson system in multi-dimensions.

Transverse Fluctuations and Their Effects on the Stable Functioning of Semiconductor Devices

Semiconductor plasma is often found in chaotic unpredictable motion which shows some anomalous behaviors providing multiple challenges to work with the instabilities in a semiconductor device. Experimental studies have shown that these instabilities give rise to fluctuations and azimuthal non-uniformities, which are usually present in the semiconductor. The energy fluctuations have also been observed in some of the cases. In this paper, we have obtained the fluctuations in velocity field by integrating the linearized governing hydrodynamic equations with RungeKutta method of order four (RK4). Then, we have come up with a mathematical formulation, where these fluctuations can be obtained from a KdV family equation with homotopy-assisted symbolic simulation. We have also obtained the relative velocity between the solitary structures for different parameters. Finally, by giving a detailed explanation of the behavior of semiconductor devices, we can study the usefulness of formulating the plasma waves in the various regime, and predict their characteristics theoretically.

Magnetosonics with Landau levels in GaAs semiconductor systems

The propagation of low frequency electromagnetic magnetosonic waves in a quantum magneto electron–hole plasma is investigated. Both of the semiconductor plasma species are magnetically quantized at equilibrium. The quantization is included through recoil effect and Landau effects on applying quantum hydrodynamic model (QHD). Analytical results of quantum hydrodynamical model are then verified numerically for GaAs plasma system.

Electron-beam–controlled deflection of near-infrared laser in semiconductor plasma

A timing method for experiments on the interaction of a near-infrared laser and an ultra-relativistic electron beam via a semiconductor plasma switch is experimentally validated. As an intermediate medium, a thin Si plate is excited by the energetic, intense electron beam to produce a semiconductor plasma, which in turn deflects counter-colliding laser light having 1 μm wavelength. An electron beam of sub-nC charge sufficiently induces the needed electron number density gradient of 1 × 1020 cm−3 per tens of μm length at the interaction point. Demonstration during an inverse Compton scattering experiment by a counter-colliding electron beam of 300 pC and 70 MeV with an Nd: YAG laser at a wavelength of 1 μm is reported.

Real-time monitoring of the plasma density distribution in low-pressure plasmas using a flat-cutoff array sensor

In the industrial semiconductor plasma processing, plasma density and its spatial distribution are critical for the understanding of discharge physics and the enhancement of the processing yield via monitoring of the status of plasma processing. Thus, real-time monitoring of plasma density and uniformity in the wafer region during wafer processing have been receiving significant attention. In this study, we developed an electrode-embedded flat-cutoff array sensor for the real-time measurement of electron density uniformity during wafer processing. We measured the spatial distribution of electron density on the wafer surface, compared it with the results measured in the bulk plasma region, and found different plasma distributions between the two where this difference can be attributed to local electron kinetics. We also performed plasma etching of amorphous carbon materials, which showed a clear correlation with the electron density distribution measured by the flat-cutoff array sensor. This indicates that the electron density distribution on the wafer surface is crucial for the process result. Thus, the array sensor developed in this study can be applied not only to measure plasma uniformity but also to predict the wafer process beforehand, making it highly significant for industrial plasma processing methods, such as virtual metrology.

Generative Adversarial Network-Based Fault Detection in Semiconductor Equipment with Class-Imbalanced Data.

This research proposes an application of generative adversarial networks (GANs) to solve the class imbalance problem in the fault detection and classification study of a plasma etching process. Small changes in the equipment part condition of the plasma equipment may cause an equipment fault, resulting in a process anomaly. Thus, fault detection in the semiconductor process is essential for success in advanced process control. Two datasets that assume faults of the mass flow controller (MFC) in equipment components were acquired using optical emission spectroscopy (OES) in the plasma etching process of a silicon trench: The abnormal process changed by the MFC is assumed to be faults, and the minority class of Case 1 is the normal class, and that of Case 2 is the abnormal class. In each case, additional minority class data were generated using GANs to compensate for the degradation of model training due to class-imbalanced data. Comparisons of five existing fault detection algorithms with the augmented datasets showed improved modeling performances. Generating a dataset for the minority group using GANs is beneficial for class imbalance problems of OES datasets in fault detection for the semiconductor plasma equipment.

Interaction of laser pulse with a quantum electron-hole semiconductor plasma

Interaction of laser pulse with a quantum electron-hole semiconductor plasma